1. Field of the Invention
The present invention relates to an optical transmission system using an optical phase conjugation device.
2. Description of the Related Art
Long-distance optical transmission systems have been constructed by using erbium-doped fiber amplifiers (EDFAs) as in-line optical repeaters. Signal attenuation due to fiber loss is periodically compensated for by the optical amplifier gain to overcome the limitation of transmission distance. Since, in such systems, signal power is maintained at a high level along the entire system length owing to the periodic amplification, the dependence of fiber refractive index on optical power can no longer be ignored. This nonlinear effect, called the Kerr effect, leads to the self-phase modulation (SPM) of optical pulses, which in turn interplays with the group-velocity dispersion (GVD), or chromatic dispersion, in the fiber, causing nonlinear waveform distortion. In order to realize long-distance (e.g. 1000–2000 km or more) signal transmission at high data transmission rate (e.g. 40 Gbit/s or more) this waveform distortion must be counteracted.
Optical phase conjugation (OPC) is a known technique for chromatic dispersion compensation. Details may be found in G. P. Agrawal, “Fiber-Optic Communication Systems”, A Wiley Interscience Publication, (1997), at paragraph 9.7. As explained by Agrawal, under certain conditions, OPC can compensate simultaneously for both GVD and SPM. Pulse propagation in a lossy optical fiber is governed by the Non-Linear Schrödinger Equation (NLSE)
                                                        ∂              A                                      ∂              z                                +                                    ⅈ              2                        ⁢                          β              2                        ⁢                                                            ∂                  2                                ⁢                A                                            ∂                                  t                  2                                                                    =                              ⅈ            ⁢                          γ              _                        ⁢                                                        A                2                                                    ⁢            A                    -                                    1              2                        ⁢            α            ⁢                                                  ⁢            A                                              [        1        ]            where A=A(z, t) represents a slowly varying amplitude of a pulse envelope, β2 is the GVD coefficient of the optical fiber, related to the dispersion parameter D by the following relation
                    D        =                              -                                          2                ⁢                π                ⁢                                                                  ⁢                c                                            λ                2                                              ⁢                      β            2                                              [        2        ]             γ is the nonlinear coefficient of the optical fiber, i.e. governs the SPM, and α accounts for the fiber loss. When α=0 (loss less case), A* satisfies the same equation when one takes the complex conjugate of eq. [1] and changes z to −z. As a result, midspan OPC can compensate for SPM and GVD simultaneously. Clearly, such case is immaterial, as fiber losses cannot be practically avoided.
In order to study the impact of the fiber loss, the following substitution may be madeA(z,t)=B(z,t)exp(−αz/2)  [3]so that eq. [1] can be written as
                                                        ∂              B                                      ∂              z                                +                                    ⅈ              2                        ⁢                          β              2                        ⁢                                                            ∂                  2                                ⁢                B                                            ∂                                  t                  2                                                                    =                  ⅈγ          ⁢                                          ⁢          z          ⁢                                                  B                                      2                    ⁢          B                                    [        4        ]            where γ(z)= γ exp(−αz). By taking the complex conjugate of eq. [4] and changing z to −z, it can be seen that perfect SPM compensation can occur only if γ(z)=γ(L−z), where L is the total system length. This condition cannot be satisfied for α≠0.
One may think that the problem can be solved by amplifying the signal after midspan OPC such that the signal power becomes equal to the input power before the signal is launched in the second-half section of the fiber link. Although such an approach can reduce the impact of SPM, actually it does not lead to a satisfactory compensation of the SPM. Perfect SPM compensation can occur only if the power variations are symmetric around the midspan point where the OPC is performed so that γ(z)=γ(L−z) in eq. [4]. In practice, signal transmission does not satisfy this property. One can come close to SPM compensation if the signal is amplified often enough that the power does not vary by a large amount during each amplification stage. This approach is, however, not practical since it requires closely spaced amplifiers.
S. Watanabe, in U.S. Pat. No. 6,175,435, considers a phase conjugator disposed between a transmission line I (of length L1) and a transmission line II (of length L2). After a series of calculations, he obtains the following equations for GVD and SPM compensation:D1L1=D2L2  [5]γ1 P1L1=γ2 P2L2  [6]where P1 and P2 denote the average powers in the transmission lines I and II, respectively. Also, D1 and γ1 denote the dispersion parameter and the nonlinear coefficient in the transmission line I, respectively; and D2 and γ2 denote the dispersion parameter and the nonlinear coefficient in the transmission line II, respectively. According to the patent, complete compensation can be realized by providing, at positions equivalently symmetrical with respect to the phase conjugator, the same ratio of the optical Kerr effect to the dispersion. An increase of this ratio along the transmission line can be attained by gradually decreasing the dispersion or gradually increasing the optical Kerr effect. It is possible to change the dispersion value by adequately designing the fiber. For example, the above ratio is changeable by changing the zero dispersion wavelength of a dispersion shift fiber (DSF) or by changing the relative refractive index between the core and the clad of the fiber or the core diameter thereof. Meanwhile, change of the optical Kerr effect can be achieved by changing the nonlinear refractive index of the light intensity. According to Watanabe, a suitable optical fiber can be manufactured by continuously changing at least one fiber parameter selected from the loss, nonlinear refractive index, mode field diameter and dispersion.
In Applicant's opinion, the use of such kinds of “special” fibers does not represent an optimal solution, as such fibers may be complex to manufacture. Further, such method does not apply to optical systems already installed, unless a substitution of all the fibers of the system is performed.
C. Lorattanasane et al., in “Design Theory of Long-Distance Optical Transmission Systems Using Midway Optical Phase Conjugation”, Journal of Lightwave Technology, vol. 15, no. 6, pages 948–955 (1997), describe a design method for suppressing the residual waveform distortion due to periodic power variation in an optical amplifier chain and to dispersion value fluctuation from span to span along a midway optical phase conjugation system. According to the authors, the amplifier spacing must be short relative to the nonlinearity length and signal pulses must be transmitted within appropriate windows of fiber dispersion. Computer simulation results reported in the article show that short amplifier spacing (40–50 km) is required for long-distance systems, whereas, for short-distance systems less than 1000 km, the amplifier spacing as long as 100 km is possible.
In Applicant's opinion, an amplifier spacing as long as 100 km also for long distance systems, having a length higher than 1000 km, is preferred, in order to reduce the number of installed amplifiers.
WO patent application no. 99/05805, to British Telecommunications PLC, discloses a method for symmetrised mid-span spectral inversion (MSSI), where the high power regions in the optical communication system are symmetrised about the MSSI means. The amplifiers are positioned so as to have the high-power regions in the two sections of the transmission link symmetrical about the mid-point of the transmission network, where MSSI is performed. These high-power regions are the length of fiber immediately after the fiber amplifier which is substantially equal to the effective nonlinear length (Leff) of the optical transmission link. The distance from the amplifier preceding the phase conjugator to the phase conjugator is LA and the distance from the phase conjugator to the subsequent amplifier is LB. The distances LA and LB are given by
                              L          A                =                                                                              L                  amp                                +                                  L                  eff                                            2                        ⁢                                                  ⁢                          L              B                                =                                                    L                amp                            -                              L                eff                                      2                                              [        7        ]            where Lamp=LA+LB is the amplifier spacing. In an example, Lamp is 80 km, Leff is 21.5 km, so that the MSSI equipment would be sited at a distance of ≈51 km from the preceding amplifier. With an odd number of spans, if it is not possible to place the MSSI equipment at a location other than an amplifier site, the author suggests to add a length of fiber Lamp−Leff kilometers long immediately after the MSSI equipment at the amplifier location. Thus a length of fiber of 58.5 km would be added. With an even number of spans, the MSSI equipment is sited immediately upstream of the optical amplifier and a length of fiber Leff kilometers long is sited immediately upstream of the MSSI equipment. The author admits it may be necessary to insert additional amplifiers to give the symmetrical positioning of the high-power regions or if the optical signal levels are sufficiently low so as to cause bit error rate degradation.
In Applicant's opinion, a positioning of the optical phase conjugator very far from an amplifier (e.g. about 50 km) has a drawback in that the optical line has to be provided with a dedicated site for the MSSI equipment, in addition to the amplifier sites. Even when lengths of fibers are added as suggested in the '805 patent application in order to place the MSSI equipment at an amplifier site, the necessity arises of providing additional amplifiers to take into account the long length of the added fiber (in particular with an odd number of spans). Such combination of long added fiber and additional amplifiers may, in turn, unbalance the power distribution along the line, so that nonlinearity compensation may be hindered.